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IMA Journal of Management Mathematics Advance Access originally published online on September 16, 2008
IMA Journal of Management Mathematics 2009 20(2):201-211; doi:10.1093/imaman/dpn025
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© The authors 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

This article appears in the following IMA Journal of Management Mathematics issue: Special Issue Mathematics in Sport [View the issue table of contents]

A ranking for the Olympic Games with unitary input DEA models

João Carlos C. B. Soares de Mello{dagger}, Lidia Angulo-Meza and Brenda P. Branco da Silva

Production Engineering Department, Federal Fluminense University, Rua Passo da Pátria 156, 22210-240 Niterói, Rio de Janeiro, Brazil

{dagger} Email: jcsmello{at}pesquisador.cnpq.br

Received on 31 July 2007. Revision received 14 August 2008. Accepted on 14 August 2008.

There is no official method to establish a final ranking for the Olympic Games. The usual ranking is based on the lexicographic multicriteria method, the main drawback of which is to overvalue gold medals. Furthermore, it does not take into account that the various sports may be of different importance. This work proposes a ranking model to eliminate those drawbacks. We use firstly a modified cross-evaluation data envelopment analysis model with weighted restrictions for each cluster. The outputs are the number of gold, silver and bronze medals and the input is a unitary constant for all countries. After obtaining a rank for each and every cluster, we build a general ranking by aggregation of the partial ones. Our model uses the results of the Athens Olympic Games.

Keywords: DEA; Olympic; ranking; weight restrictions; unitary input


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